Stopping Distances

… written in collaboration with Ruth Casey and Sam Gough.

Distracted driving is any non-driving activity a person engages in that has the potential to distract him or her from the primary task of driving and increase the risk of crashing.
~
From D!straction.gov
The Official US Government Website for Distracted Driving

A typical rule for the distance you should follow behind a car is given by the “three second rule.” To determine the right following distance, select a fixed object (a tree, a sign, an overpass ..) on the road ahead. When the vehicle ahead of you passes the object, begin counting “one one thousand, two one thousand, three one thousand.” If you reach the object before you complete the counting, you’re following too closely.

• When you see an object in your path, can you stop your car instantly?
• What happens between the time you realize that something is in your path and when the car actually stops?
• How much distance has been covered before the car has stopped?
• How does your reaction time affect these distances?

As an introduction, watch Vehicle Stopping Distance from teacher’sdomain.org or Think! – Slow Down which is embedded below.  (Warning…it is tough to watch.  A dummy is used, but you should preview before you show it to students.  I like it because you can see the screeching tires and the struggle to stop.)

If you are interested in the physics, check out the Vehicle Stopping Distance Calculator from Computer Support Group and their online division, csgnetwork.com.

For an experiment of calculating your reaction time, do the math.

Let’s look at the data.

Suppose you want to visualize the pattern in the distance traveled while reacting versus the speed of your car.  Do I travel the same distance while I’m reacting no matter the speed or does the speed influence the distance traveled just while reacting?

• What does this pattern tell us about reaction distance traveled vs. speed?
• Can you find the mathematical model for these data?
• What is the slope? What is the meaning of the slope?
• Is this direct variation?
• Which of our learners can find success with this?

How about the pattern in the distance traveled while braking versus the speed of your car?

• What does this pattern tell us about braking distance traveled vs. speed?
• Can you find the mathematical model for these data?
• What is happening with the slope?
• Which of our learners can find success with this?

Now, how about the pattern or relationship between the total distance traveled while stopping the vehicle vs. the speed?

• What does this pattern tell you about the total braking distance vs. speed?
• Can you find the mathematical model for these data?
• What is happening with the slope?
• Which of our learners can be successful with this?

I don’t want to give away the mathematical models; I want you to have time to consider and think about the mathematical models.  If you need or want a hint, please leave a comment below and I’ll write you back.

8 thoughts on “Stopping Distances”

1. Bo, We do not yet do this lesson in Algebra I. It is totally doable, mathematically for our learners. It is a proposed topic of discussion for our 4th Period Science-Math PLC.

Our hope is to “do” the lesson together to be students, practice with our laptops to prepare for 1:1 next year, integrate our studies, find connections between math and science, and – if that is not enough – connect our existing Essential Learnings vertically and horizontally through our courses.

What do you think?

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